As @AndrewThompson wisely mentioned, the use of multiple JFrame is a
bad practice. In this case a (non-)modal dialog would be a better
choice.
Now let's assume you choose non-modal dialogs, then you still having
the same problem. There are several ways to solve it but essentially
you need to keep a reference to the frame/dialog which opened the
calendar's frame. Even better, you can use interface

It looks like the object firing the event is different than the object
listening for the event.
fld.on('paste', me.pasteFromClipboard,fld);
fld.on('click', function(evt,target){
fld.fireEvent('paste'); // Trigger Paste Event.
},fld);
Now, both the firing and listening is tied to the fld

Since there is no object of jframeA I don't understand how to close
this frame from jframeB on click of a button.
If you expect to act on an object, then you need to save a reference
to it.
Login jframeA = new Login();
// ...
jframeA.setVisible(false);
jframeA.dispose();
jframeA = null;

Generally speaking, there is no need to use jQuery to access Ext.NET
components on client side.
Each component is shared in the Ext.NET namespace which is "App" by
default. A component's id is a key in the namespace.
To retrieve a TextField's value, please use the getValue method.
var value = App.TextField1.getValue();